Phononic Bandgaps

This is an educational project started while guiding our advanced undergaduate lab. The work is in preparation for submission to AJP. It is a common task to find resonances in an acoustic cavity. This system is analogous to atomic and electronic systems and it is natural to look for phenomena that are well known for such systems. This is especially true given that it is often hard to demonstrate or have a hands-on experiment for students showing he behaviour of atomic and electronic systems. The analogies with sound can sometimes be a helpful replacement.

By coupling different resonances to eachother with an adjustable interaction phenomena such as level splitting, avoided crossings, and badgaps are well known in electronic and atomic systems. Can we realizee these phenomena in sound?

The answer is yes. The figure shows the level splitting route to phononic bandgaps. One cavity has resonances. In two cavities separated by a holed disk these resonances split in two. In three cavities the resonances split into three, etc. For six cavities the resonances are not resolved anymore and bands and bandgaps form.

Bandgap graphs of differing frequencies